Question

On a coordinate plane, an absolute value graph has a vertex at (0, 0).

Complete the statements for the graph of ( f(x) = |x| ).

The domain of the function is _______.

The range of the function is _______.

The graph is _______ over the interval (0, [infinity]).

The graph is _______ over the interval (–[infinity], 0).

Answer 1

The function f(x) = |x|, with a vertex at (0, 0), has a domain of all real numbers (-∞, +∞) and a range of all non-negative real numbers [0, +∞). The graph is increasing over (0, +∞) and decreasing over (-∞, 0).

Step-by-step explanation:

Absolute Value Function Characteristics

The graph of the function f(x) = |x| is a key concept in high school mathematics, specifically in the study of functions and their properties.

The domain of the function f(x) = |x| is all real numbers, since absolute value is defined for any real number. Therefore, the domain can be written as (-∞, +∞).

The range of the function is all non-negative real numbers, as the absolute value of any real number is always zero or positive. Thus, the range is [0, +∞).

Over the interval (0, +∞), the graph is increasing since as x gets larger, |x| also gets larger.

Over the interval (-∞, 0), the graph is decreasing because as x gets smaller (more negative), |x| gets larger.

This function demonstrates the properties of two-dimensional (x-y) graphing, where the horizontal x-axis represents the independent variable, and the vertical y-axis represents the dependent variable, f(x).